Download Section 9.3 Notes - Verona Public Schools

Section 9.3- Solving Quadratic Equations
Essential Question: How is graphing a quadratic equation similar to solving it algebraically?
Do Now:
1. Use the equation below and solve it using two different methods.
𝑥 2 − 25 = 0
a. Solve the equation below by factoring.
b. Solve the same equation using a different algebraic method.
2. Can you take the square root of each number? Explain.
a. √49
b. √−49
Solving Quadratic Equations by Graphing

The solutions to a quadratic equation represent the ____________________________.

There are three cases when graphing quadratic equations.
o
A parabola can have AT ____________, _____ solutions.
o
It may also only have _______________________________.
o
There may also be instances where there is __________ _______________. This
means there are no _________________________________.
Example 1: Solving by Graphing
Graph the following quadratic functions. What are the solutions of each equation?
a. 𝑦 = 𝑥 2 − 16
Solutions: _______________________
c. 𝑦 = 𝑥 2 + 1
Solutions: _______________________
b. 𝑦 = 𝑥 2
Solutions: _______________________
d. 𝑦 = 𝑥 2 − 1
Solutions: _______________________
Example 2: Solving Using Square Roots
What are the solutions of each equation?
1 2
𝑥
4
a. 3𝑥 2 − 75 = 0
b.
c. 𝑥 2 − 36 = −36
d. 3𝑥 2 + 15 = 0
Example 3: Choosing a Reasonable Solution
−1=0
Group Work:
Solve each equation by graphing the related function OR by finding square roots.
1. 𝑥 2 − 25 = 0
3.
2 2
𝑥
3
−6=0
2.
2𝑥 2 − 8 = 0
4. 𝑥 2 + 36 = 0
5. You have enough paint to cover an area of 50 𝑓𝑡 2 . What is the side length of the largest
square that you could paint? Round your answer to the nearest tenth of a foot.
6. What do you notice about all of the values for ‘b’ when you are able to solve a quadratic
equation using square roots?
HW: p. 564 #9-17 odds, 20-28 evens, 40